Geodesic
Accumulation of Switchings in Distributed Parameter Problems
Contemporary Mathematics. Fundamental Directions, Optimal control, Tome 19 (2006), pp. 78-113

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In recent tens, optimal control theory for distributed parameter systems is actively developed; among them, an important place is occupied by the class of systems describing oscillation processes. This work studies linear control distributed parameter systems of hyperbolic type. The minimization problem of a quadratic functional on the trajectories of the system is considered. By using the Fourier method, the problem is reduced to studying optimal solutions for a countable control system of ordinary differential equations. For Galerkin's approximations of this system, it is proved that the optimal control is a chattering control, i.e., it has infinitely many switchings on a finite interval of time. The construction of the optimal synthesis uses the results of the theory of singular regimes and regimes with with more and more frequent switchings. 
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     author = {M. I. Zelikin and L. A. Manita},
     title = {Accumulation of {Switchings} in {Distributed} {Parameter} {Problems}},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2006_19_a3/}
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M. I. Zelikin; L. A. Manita. Accumulation of Switchings in Distributed Parameter Problems. Contemporary Mathematics. Fundamental Directions, Optimal control, Tome 19 (2006), pp. 78-113. http://geodesic.mathdoc.fr/item/CMFD_2006_19_a3/